Three British residents held at the US Guantánamo Bay detention facility in Cuba without charge for more than four years have been detained after arriving back in the UK tonight.

Libyan-born Omar Deghayes and Algerian Abdennour Samuer were arrested under the Terrorism Act shortly before landing at Luton airport around 7pm and taken to a central London police station for questioning.

The third man, Jordanian Jamil el-Banna, was detained but not arrested and taken to a police station in Bedfordshire.

The three men were on board a chartered aircraft with a civilian flight crew and a doctor.

Officers from the Metropolitan police's counter-terrorism command were on the flight along with uniformed officers from the Met, who acted as an escort team at the request of the Foreign Office.

Earlier, the three men's lawyer, Clive Stafford-Smith, described their arrival in the UK after being released from the detention facility as "a wonderful day".

"We fully expect that the British government, after they have questioned them, will let them go home to be with their families for the Muslim festival of Eid, which is today and tomorrow," said Stafford-Smith.

He revealed that the three men had agreed to "voluntary security arrangements", which they are not allowed to disclose, required by the UK authorities. But they fall well short of the control orders imposed on some terror suspects in the UK, he added.

Stafford-Smith rejected concerns about any potential "national security risk" the men might pose.

"We have had 10 of our clients come back to Britain and the Americans said on each occasion they were dangerous people and on each occasion our clients have caused no trouble," he said.

El-Banna's wife, Sabah, released a statement through her Brent East MP Sarah Teather, who had helped campaign for his release, in which she expressed her hope that they could now be a "normal family".

"After five years of waiting, a lot has happened to me and my children," she said. "It has been a very difficult time, but thank God it is now finished and we have justice at last."

Deghayes' sister, Amani, said she was extremely relieved to hear the news of her brother's release and said he had been on the receiving end of "brutal and illegal treatment".

She said: "Our family has always said that Omar was totally innocent - one of the hundreds of people taken to Guantánamo by the Americans for no good reason."

Teather said the US had tortured El-Banna - exposing him to extremes of temperature, beatings and "appalling and unrepeatable threats to his wife" - and said it would be a "grave, grave injustice" if he were not allowed to remain in Britain.

"There is nowhere else for him to go," she told Sky News.

Amnesty International's UK director, Kate Allen, welcomed the return of the men, who she said should be treated "first and foremost as victims", but called for the release of other prisoners with "ties to Britain" in the detention facility.

The release of the three leaves two remaining British residents - Saudi national Shaker Aamer and Ethiopian-born Binyam Mohamed - at the notorious prison camp, according to the Foreign Office.

The foreign secretary, David Miliband, said in a statement last Thursday that he had been petitioning the US on behalf of all five men. Miliband said discussions regarding the release of Aamer were no longer "active" but the ministry was still in talks over Mohamed's case.

Amnesty is also campaigning for the release of Ahmed Belbacha, an Algerian man who, it says, has permission to remain in Britain pending a decision on his asylum application.